3-2/9b=b-7

Solution for 3-2/9b=b-7 equation:

3-2/9b=b-7

We move all terms to the left:

3-2/9b-(b-7)=0


Domain of the equation: 9b!=0

b!=0/9

b!=0

b∈R


We get rid of parentheses

-2/9b-b+7+3=0

We multiply all the terms by the denominator


-b*9b+7*9b+3*9b-2=0

Wy multiply elements

-9b^2+63b+27b-2=0

We add all the numbers together, and all the variables

-9b^2+90b-2=0

a = -9; b = 90; c = -2;
Δ = b2-4ac
Δ = 902-4·(-9)·(-2)
Δ = 8028
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8028}=\sqrt{36*223}=\sqrt{36}*\sqrt{223}=6\sqrt{223}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{223}}{2*-9}=\frac{-90-6\sqrt{223}}{-18}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{223}}{2*-9}=\frac{-90+6\sqrt{223}}{-18}
$